"Following the progress that has been made in the negotiations on security with the Palestinians, President Mubarak has invited Sharon and Abbas to a meeting next Tuesday at Sharm al-Shaikh," a statement said.
"The prime minister has accepted this invitation," it added.
Abbas also accepted the invitation to the summit at the Red Sea resort, a senior Palestinian official said on Wednesday.
The talks will be the highest-level Israeli-Palestinian meeting in nearly four years of conflict.
A summit has been expected since Abbas, who was elected to succeed the late Yasir Arafat last month, managed to coax a de-facto truce from resistance fighters waging an uprising.
Israel responded by cutting back on military operations.
Sharon's office said the invitation to the summit was delivered by Egyptian intelligence chief Umar Sulayman on a visit to Jerusalem.
Meanwhile, Syrian President Bashar al-Assad arrived in Jordan on Wednesday for a brief visit expected to focus on Syria's role in the Israeli-Palestinian peace process.
Jordan's King Abd Allah is keen
for Syria to join peace talks
Jordan's King Abd Allah II met al-Assad at Amman airport and they headed straight for the royal palace in Amman.
Jordan's official Petra news agency said the visit of a few hours would deal with "current developments in the region".
But Jordan's government has been pushing for Syria to join Egypt in negotiating a Palestinian ceasefire as several Palestinian factions have offices in Damascus.
However, Israel has voiced opposition to involvement by Syria.
Amman and Damascus have different approaches to Middle East peacemaking.
Jordan, which has a peace treaty with Israel, advocates a moderate line, while Syria adopts a more hardline approach to solve the conflict.
Jordan and its northern Syrian neighbour have had bumpy relations under their late leaders, partly because of Jordan's 1994 peace treaty with Israel.
But ties improved when Abd Allah and al-Assad took over power from their fathers in 1999 and 2000 respectively.
Wednesday's visit is al-Assad's first to Jordan since April last year.